Keele (1974-04 AES PublishLow-Frequency Loudspeaker Assessment by Nearfield Sound-Pressure Measuremented) - Nearfield Paper

7/24/2019 Keele (1974-04 AES PublishLow-Frequency Loudspeaker Assessment by Nearfield Sound-Pressure Measuremented)

1/9

Low-F

re

que

n

cy Louds

p

eak

e

r Assessme

nt b

y Nea

r

fi

e

ld

Sound-Pressure Measurement*

D. B. KEELE

, JR.

Electro

-

Voice, Inc

.

, Buchanan, Mich

.

49107

A loudspeaker test technique

is

described which depends on nearfield pressure mea

-

surements m ade in a nonanechoic environment. The technique allows extremely simple

measurements to be made of frequency response, power response, distortion

,

and

e le ct ro acou st ic al e ff ic ie ncy.

GLOSSARY OF SYMBOLS

r

distance fr

o

m pressure sample point t

o

center of

piston

a

radius of circular radiator

R

_ dc resistance of driver voice coil

ao

radius of diaphragm, = _

/S

D

/

_

r E

surface area

ay

radius of circular vent

,

= 5

/S

v

/

_

r S

D effective projected surface area of driver diaphragm

c

velocity of sound in air, = 343 m

/

s

S

v cross-sectional area of vent

e

in voltage applied to driver input SPL sound pressure level

,

in dB re 20

/x

N

/

m 2

[

frequency, in Hz

U

o output volume velocity of acoustic radiator

[

_ Helmholtz resonance frequency of vented box 3. wavelength of sound in air, =

c//

]

s low-frequency cutoff (--3 dB) of speaker system ,

/

nominal power transfer efficiency, =

P

a

/P

_

I

o acoustic intensity

,

in power per unit area

,

*

/

o reference efficiency defined for radiation into a

:

p

a

/

(2

p

o

c

) for a plane wave half-space free field

k

wave number, = 2_

r/

3. =

to/c p

o density of air, = 1.21 kg

/

m s at 20 C

p

peak sound pressure c

o

radian frequency variable

,

= 2 _-

[

.

P

i* peak sound pressure in farfield of acoustic radiator

Pz

peak sound pressure in nearfield of acoustic radi- I

N

T

R

OD

UC

TIO

N

: The low-frequency evaluation of a

ator loudspeaker systemwith respect to frequency response

P grins root mean square sound pressure in nearfield of distortion, and power output has traditionally required the

radiator, =

pzd

V2 use of a large and expensive anechoic chamber or a cum-

P

R peak Sound pressure on axis of piston at distance

r

bersome and often equally costly open-field outdoor test-

P

a acoustic output power lng Site. Recently, Small [1] pointed out that valid measure-

P

_ nominal electrical input power ments could be made at very Iow frequencies in any rea-

Q

ratio of reactance to resistance (series circuit) or sonable environment by sampling the pressure inside the

resistance to reactanc e (parallel circuit) enclosure

Q

B

Q

or cabinet at

/

_ considering all system losses

1 Even the large anechoic chamber at Electro-Voice is not

much good for low-frequency measurements below 40 Hz in

the fartield (beyond 10 ft (3 m) from the speaker system

* Presented May 15, 1973, at the 45th Convention of the being tested). EV engineers ha

v

e resorted to Small's technique

Audio Engineering Society, Los Angeles. numerous times tomeasure response below this frequency.

154 JOURNALOFTHEAUDIOENGINEERINGSOCIETY


2/9

This paper describes a very simple measurement method strength Uo radiating from an infinite baffle [2, Eq. (7.40),

which is based on measurements taken in the nearfield p. 165]. Eq. (2) exhibits the well-known inverse relation-

outside the enclosure and, like Small's method, may be ship between pressure and distance.

used in any environment. However, this method does not

require the frequency-dependent signal processing cir-

N ea rfie ld P ress u re

cuitry of Small's method and is accurate over a wider

frequencyrange. At points very close to the center of the pistonwhere

r

< a and for

low frequencies such that ka < 1, Eq. (1) can be shown to This surprising result shows that for low frequencies

converge to (

ks

_ 1) the nearfield sound pressure is directly propor-

tional to the farfield sound pressure. The relationship de-

Pa _ __t k Uo (2) pends only on the ratio of the piston radius to the farfield

2 _r

r

sample distance and is independent of frequency. From a

practical measurement standpoint, the nearfield sound

where Pv is the peak axial pressure measured at distance r pressure P2_and volume velocity Uo are essentially inde-

in the farfield of the piston. This relationship of course is pendent of the environment into which the piston is radi-

the familiar equation that gives the farfield low-frequency sting [1, p. 29]. This means that valid inferences can be

sound pressure for any generalized simple sound source of made about the low-frequency farfield anechoic operation

A

PRIL1

97

4,VO

L

U

M

E22,

N

U

MB

ER3 1

55


3/9

D. B.

KE

E

L

E, J

R

.

of a particular speaker system from nonanechoic measure- face of the piston than 0.1 l

a

. For low frequencies

,

farfield

ments of the nearfield sound pressure, conditions exist for distances beyond 2

a

.

A parallel derivation for the case of a piston radiating

intoa fullspaceat lowfrequenciesyields ,

O

I I _'.. A

X

I

A

L

r

p

_

r -

-_

P

F. (6) ]

_'-

t

'--'-,_B

; u

t

-

_l -

--

J:

:

== _

,

P

R

ESSURE

PR ,,., -10 '

MeasuringDistance P

To investigate more fully the axial sound pressure de- d B

pendence on measuring distance

,

Eq. (1) is examined in - .04 .08._ .2 .4 .

s

_ 2 4 e _0

more detail. For distances from the piston less than 0.75 r

a

2

/

X, plane waves are radiated which are contained essen- a

Fig. 4. Sound pressure along axis of a rigid circular piston

tially within a cylinder of diameter 2

a

[3, p. 187]. Fordis- radiating into a half-space freefield, for frequencies low

tances beyond 2

a

2

/

X approximately spherical divergence enough such that

ka

< 1 (loudspeaker piston range).

is found to hold, where the pressure falls inversely as the

distance. For frequencies equal to or higher than the fre-

quency where

a

=

2

_(

ka

_ 2)

,

the pressure is found to go Flat Piston Pressure Distribution

through a series of maxima wi

t

h intervening nulls as the

distance from the piston's surface is increased. For low The analysis so far has considered only measurement

frequencies such that

ka

< 27r the only pressure null oc- points near the center and along the axis of a flat circular

curs at

r

= oo. A plot of Eq. (1), normalized to the maxi- piston. In general, the nearfield sound pressure distribu-

mum axial pressure for several values of

a/

X, is in Fig. 3. tion over the surface of a piston is very complicated,

especially for the higher frequencies (

ks

> 2_

r

). Zemanek

, [3]

,

in an excellent numerical analysis, presents the fine

___x_

[

_x

/

details of the nearfield pressure distribution for a circular

o j

2

._.._. piston operated in this higher frequency range.

-to

/

'% -

Fortunately

,

in the low-frequency piston range of oper-

///

a I

]

1

/

_ ation (

ks

< 1) the nearfield pressure is very well behaved

-20 ) a=4_ I and smoothly distributed. For

ka

_ 2

,

McLachlan [4,

o _ _, p. 49]has evaluatedthe exactexpressionfor the pressure

_

/_//_

-_%_a=

2

_1 distribution at the surface of a rigid circular piston. Fig.

5,

which shows the radial dependence of pressure magnitude

-

to for

ka

= 0.5 and 2, displays some of McLachlan's work.

- 2

0 .

b

)

Examination of Fig.

5

reveals that the low-frequency near-

A

X

IA

L

field pressure varies quite gradually as a function of sur-

P

_

.,

O

.... _ - '_.RESS face position reaching a maximum at the piston center.

tO _

dB / i=/X O

/

c -

--2

0

/

-- -

.

_

-2

O LEVEL .4 ka.. _ _

----- - J _ _ _ 1 dB.

j 6 _

t

9

-8

i _a=.75/_ I

-

2o

_ (d

) o

.

2

.

4

.

e

.

8

t

o

'' .a4 .1 .4 . r I 4 10 4

0

CENTER X_ _

- _. OUT

S

ID

E

a EDG

E

F ig. 5. N orm alized nearfield sound pressure distribution on

Fig. 3. Sound pressure along axis of a rigid circular piston surface of a rigid circular piston vibrating in an infinite flat

radiating into a half-space freefield for several values of

a/

X. baffle, for

ka

= 0.5 and 2. The distribution exhibits circular

symmetry and is only a function of the radial distance from

If the upper frequency of measurement is limited such the center to the edge of the piston (after [4]).

that

ka


4/9

LOW-FREQUEN

C

Y LOUDSPEAKER ASSESSMENT BY NEARFIELD SOUND-PRESSURE MEAS

U

REMENT

direct-radiator cone speaker systems have correlated ex- substitution of PN = 3v/'_PNrmsyielding

tremely well with measurements made by other conven-

tional means. In every case the nearfield sample was taken

P

x --

SD

p

_

r

rms2. (10)

where the nearfield pressure was at a maximum, i.e., 2poe

usually at a point near the cone's apex or speaker's dust

This equation indicates that for the low-frequency pis-

dome. ton range operation of the radiator (ka _ 1), the total

radiated sound power may be assessed by a simple mca-

Radia

t

ed Sound Power

surement of the nearfield sound pressure at the center of

The total radiated sound power output of an arbitrary the piston. Fig. 6 plots this relationship for acoustic power

acoustic source radiating into a half-space is found by output in watts versus p_rrms in dB re 20 p2q/m 2 for sev-

integrating the intensity function over a hemisphere eh- eral values of piston size.

closing the source. If the radius of the hemisphere is large

Efficie

n

cy

4 The power conversion efficiency of the transducer is

given by the ratio of the acoustic output power to nominal

electrical input power for radiation into a specified en-

vironment (taken here as half space or 2 *rsr). For the spe-

cific case of a loudspeaker driver with voice coil dc resis-

tance R_, the nominal electrical input power P_ is defined

.

as the power available across

Rz

for applied source voltage

e

in [

5

, p. 386]:

P_ = ein2/ Rl_ . (11)

ACOUSTIC .l The efficiency may be computed in terms of the nearfield

POWER pressure and input voltage by dividing Eq. (10) by Eq. (11),

OUTPUT .04 giving

P

A

PA SD RB P_Vrrn2 (12)

WATTS

*

/

= _B --

2 po c e

in

2

.01--

This relationship yields efficiencies that are within 1 dB

2 .004-- of the true efficiency for ka _ 1.6 (assuming the piston

P

A=S

Pnrms operates rigidly in this region). Fig. 7 plots this relation-

2

)oC ship for the specific situation of 1 volt rms applied to a

(

H

A

L

FSPACE,

=

20

'

C) driver whose R B is 10 ohms, for several values of piston

.00

1

size. For other values of

R

B, the values of ,

/

obtained

from this figure can be scaled accordingly (if RB is higher

or lower than 10 ohms the efficiency is higher or lower in

direct proportion). An efficiency curve has been included

100 110 120 130 14

0

in Fig. 7 for a piston of 10 in2 (64.5 em") true effective

PNrmsSPLdB (re 2x10$

N/m2l

area to ease computations of efficiency for radiators of

other sizes. Thus the efficiency of any driver is the value

Fig. 6. Total radiated sound power Pa of a rigid circular given by this curve multiplied by the ratio of actual piston

piston radiating into a half-space to nearfield sound pressure area to 10 in2 (64.5 cm 2) and again by the ratio of actual

level measured at points close to center of piston, for low fre- voice-coil resistance to 10 ohms.

quencies such that ka < 1. The following piston sizes are

plotted: 10-in2 (64.5-cm 2) effective (actual) area, 8-in (20.3-

em) advertised diameter (6.2-in (15.7-cm) effective diameter), Frequency and Power Response

12-in (30 5-cm) advertised diameter (9 8-in (269-cm) effective

diameter), and 15-in (38-cm) advertised diameter (12.6-in (32- As stated earlier, Eq. (5) indicates that the relationship

em)effectivediameter), between near and far sound pressures depends only on

enough so that all points on the hemisphere are in the far- two length constants and is independent of frequency

field of the source, and if the source is radiating essen- (for ka _ 1). Therefore, low-frequency response can be

tially omnidirectionally (ka _ 1), the radiated acoustic measured quite simply by plotting the nearfield pressure

power is givenby (in dB) versus frequency. Total acoustic power output

versus frequency can then be derived using Eq. (10) or

ff,s

o = p.r2 . (8) Fig. 6.

po c

Solving Eq. (5) for Pr and substitution into Eq. (8) Distortion

yields Becauseof relation(5),completelyvalidmeasurements

Pa ,r a2 SD of low-frequency harmonic distortion can be made in the

. p_e -- pN2 (9) nearfield and these should correlate well with an identical

4 po c 4 po c set of measurements in the farfield if all distortion cum-

where

S

D is the effective area of the piston, ponents are within the specified frequency limit. Some-

Eq. (9) may be rewritten for the case of rms pressure by what lower nearfield distortion values are to be expected

APR

I

L1974,

VOL

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5/9

D. B. KEELE,JR.

where distortion harmonics exceed this limit. The rela- sure. Assuming roughly equal individual driver directional

tively high SPL found in the nearfield of a piston can characteristics and equal farfield pressure contributions

actually aid distortion m easurements because the acoustic (equal efficiencies), the nearfield SPL is found to be in-

signal-to-noise ratio is much improved. In most cases, versely pr

o

portional to the linear dimensions of each

meaningful distortion tests can be made even in a noisy driver (i.e., the tweeter, which is the smallest, has the

laboratoryenvironment, highestnearfieldSPL).

4

0

Ve

nt

e

d

B

o

x

The nearfield pressure technique is found to work well

for m easurem ent of the low-frequency characteristics of

1

0 the vented enclosure system. The complete system opera-

NoMiNAL

tion for a multiway vented-box system can be assessed in

'POWER 4

the same manner as the closed-box system by measuring

the nearfield pressure of each driver individually. The

TRANSFER

following comments apply to the piston-range operation

EFFICIENCY of the woofer mounted in the vented enclosure.

The vented-box system frequency response can be eval-

uated using the nearfield method. Benson [6, p. 47] dis-

playsthe theoreticaloveralllow-frequencyesponseof a

B

.2 4th-order Butterworth (Thiele's alignment no. 5 [7]) vented

% system,along with the individualcontributionsof the

.1 vent and driver. Fig. 8 is a reproduction of these data.

The driver diaphragm response is found to exhibit a

SDR_,P_n,m, 04 null at the vented-box resonance frequency JB. The depth

_Y_=

2

_

OoC

e_, of the null is found to be directly related to the total

cabinet losses QB [8, p. 414]. A simple measurement of

{HALFSPACE,T-----aoC, RE=IO_,_., the driver nearfield SPL frequency response reveals

e ln= V rme

100 110 120 130 the value of fB by noting the frequency of the null. The

P.rm SPL dB (re2xl0'5 N/m 2) driver reference efficiency */o can be derived (with the

aid of Fig. 7) by noting the nearfield SPL in the level

Fig. 7. Relationship between nominal efficiency of a loud- response region above 2

)

Bwith 1 volt rms applied.

speaker driver operating as a rigid piston and radiating into a The vent s contribution to the total system output can

half-space and nearfield sound pressure level, for frequencies be likewise determined by a nearfield response measure-

low enough such that ka _ 1.The graph is normalized to unit

input voltage (e,_ -----V rms) and voice coil resistance Rs of ment of the vent. For best results, the measurement micro-

10 ohms. Refer to Fig. 6 for description of piston sizes, phone should be placed in the center of the vent, flush

with the front surface of the cabinet. Practical measure-

ments of the vent nearfield output in the frequency range

above /B reveal that the measured response is contami-

LOUDS

P

EAKER

S

YSTEM MEASUREMENTS

hated by crosstalk from the diaphragm. Valid nearfield

The nearfield pressure measurement technique is a very SPL measurements of the vent can only be made for fre-

powerful tool for evaluating the performance of assem- quencies less than about 1.6/_.

bled loudspeaker sy stem s. A n earf ield p ressure frequency

response measurement of each driver in a system (both in O

,

OV

E,^,L

and out of the system)can answera wholehost of ques- [ i_,r

tions

concerning low-frequency bass response, overall

-2n

lv__

-

_

_ /

iii

[

DfA_

RA

[_' _ ...... L _

system frequency response, system efficiency, relative

efficiency, and levels between drivers, distortion, etc. dB __/_../_[__ i i I _

-4

0

Closed Box 6o', /, , , , , .... t*

The woofer's nearfield

pressure

frequency response,

-

.1

.

2

.4

.8 1 2 4

8

1

0

measured with constant known drive voltage, is a direct _

f

s '

analogue of the frequency response that would be mea-

sured in an anechoic cham ber (half-space loading) for Fig. 8. Theoretical sound pressure frequency response of a

the piston range of operation. Figs. 6 and 7 can be used vented undamped-enclosure loudspeaker system aligned so

in this case to plot system acoustic power output and that the overall response conforms to a 4th-order Butterworth

h ig h-p ass f ilter f un ctio n (Thiele a lig nmen t n o. 5 [7 ]). I nd iv id-

efficiency as a function of frequency (knowing ein, Rd, ual farfield pressure responses are shown for the contributions

and resultant nearfieldSPL). of ventanddiaphragm(after[6]).

In-box measurements of nearfield SPL can be taken of

all the drivers in a multiway system with crossover con- The individually measured nearfield responses of the

netted to provide data for computation of relative levels, vent and driver may be used to construct an approximate

approximate overall frequency response, efficiencies, and farfield overall system frequency response. Eq. 5 must

crossover frequencies. Eq. (5) can be used to compute again be used to adjust the relative levels of diaphragm

each individual driver s contribution to the farfield pres- and vent, according to their respective diameters, before

158 JOURNAL OF THE AUDIO ENGINEERING SOCIETY


6/9

LO W F REQ UE N C Y LO UD SP EA K ER A S SE S S M E N T BY N EA R FIE LD S O UN D P R ESS U R E M E A SLIR EM EN T

the responses can be summed. For example, if the vent --25, and --30 dB (referred to nearfield pressure) were

diameter is one half the effective diameter of the chosen (

r

=0

,

0.6

a

, 1.4

a

, 2.7

a

, S

a

, 8.9

a

, and 15.8

a

, from

driver diaphragm, the driver output must be increased Fig. 4). Fig. 9 shows the results of these measurements.

by 6 dB before the outputs can be summed. The summa- The fgure indicates close agreement with theory for all

tion implied here is of course vectorial, where both mag- frequencies less than about 2 kHz (

kb

_-_ 1.4). Note the

nitude and phase must be considered. It is noted, how- large variation in signal-to-noise ratio between the re-

ever, that the port and cone are roughly in phase above spouses in Fig. 9 and the improvement gained in the

[B and out of phase below

[

B (for high cabinet

Q

). At nearfield (

r

= 0).

]B the system output is predominantly that of the vent.

For situations where crosstalk is not much of a problem, --_=L--,. _=

:

_L ____+___-w-

:

_

one might even perform the indicated summation by gO = 2V

,

m,:===='

-

':,

v

,=_-

using two microphones (one for the diaphragm and one 80- _.

:

}: (}? ? _>_-_:_'J'-:_j_

:

_---J?3 IV h-

,:i_t ,::':, :,:

:

; i

i

-J:_it

for the vent)and then combining the microphone outputs ii'iii_}_

:

-?

FARFIELD -*

z :

i :1"' = x4: :

by the use of a microphone mixer with input gains set 70

-= -- -[

:

_1-',_:t7:i---4-:[YI::

x

appropriately. --,-:_:::__: r- =_..... : :t:-

v

::4:

r-- _

-: T

.

:- :

:: ,1{_1 I'

EXPERIMENTAL MEASUREMENTS

Measurements were taken experimentally on several l l

O-

:

-=_

:

i_t' '_:i_J:

-

::

different types of systems to verify the theory and tech-

1OO 'b)_[i_ ii; _ :=, FULL--SPACE:

[-[_[=

niques put forth in this paper. A list of the measuring =_ _...._--,_L_.L_lt,t?....

equipment used, along with a brief explanation of how ..... ........

:

:_:_ _['iJ}-=; 0}=l_l?_it; 2

[

:1_

- :: 'V ' _:.::

w

=_

:

:

:;

i:, -::_: -- : ii

_

:

J--

2

......... J

::

_

:t=

J=_

x

,

:

_Ij.=

L

-_J=[

_

i_:_=_5

:

-

Small's box-pressure measurement method [1] was imple- go :3 Fl .... is.,C-_-_x':_

.

_,____ ,,-,_"xfi'_?_

_ : :

mented, is outlined in the Appendix. $PL ........ $ _

r

t ....... _ '_[: _-_ ] r _::

80 :-----'_.i4.iJ__=_-_::t r_, :-_: =:4? _i:_

-- ::l:::i:i

/

:: :

:

12 : FAR,FI

E

LD

:-

'i

T

T [?

-

-.:J: :

:=_

-;

/

:. i

7

-

i_

-

:

1_

_

-

-

:

.=

--

2=

-: [

--

_

SPL and Frequency Response Versus Distance dB 70 =,O):/t .... _. ::=:_:1,tli[ ..... _I=::N =....

:,

v

_j:;;I=

:

_-.:

:

HALF-SPACE :i:l,[x .____

Eqs. (5), (7), and Fig. 4 were checked by making ex- 5 _/i:Jl:::ii -[_ _ =;zl :l l_ _[:-=t=_-:il:l:ii

perimental measurements in the anechoic chamber on a ,, .........................

4-in (11.4-Cb) (1

-

in (3.8-cm) effective piston radius) _=_v

t

m

,,

full-range driver in a closed box, flush mounted in the 110 _[-t. lt_ =:i_.=_Izl:-E_L_=_=t---_

:

:-

I --:: :_t,,dP

J

:

/

;tH t

:

: LAII_J_:_-: _:: NEAF_FIELD_ : ._i_i _

center of an 8- by 4-ft (2.4- by 1.2-m) baffle board --121:_, ..... _:_l_:___=l=___ti---::::

(roughly a half-space for distances not far from the 1

OO t._-__[_:i.ii__=t__.=_=__t.i:t:

:

.,_l-

-

_=t=_=_.

board). The 395-in a (6473-cm a) closed test box was .: ?t

.

Ij_: J=t_:_F_

-

i-_.[t

V

=_[_5_

roughly cubical, with external dimensions of 7.75 by 8.25 =____j:_=________= =155_ _. __

z

by 8.5 in (19 by 21 by 21.7 Cb). The driver was mounted :==_=__v_m._ __:_ =\ [=__: _:_i_

from the outside, off center

,

on the 8.25- by 8.5-in (21- t

:

t=1_-_6

-

-_=I-_ ...... -_:_

_ ?SV_.-_0_ ---

by

21.7-cm) face. : _----

/

,_[[-

z

-[=i_

b

_

-_

_

r T I

.

11_i

.

J

.

;

i

T

-

_ _

.

=

.,

:i

: -

r

.: -

-y- ....

t

lVrm, _;nl_- r=

6

...._,_g

r

?'-I iii;ii :-_/ ,,,..

/..........

_ _:_U_

_ _ _'r - - _',_--:--:__'_ _ i I ',_J

5PL -J_-_-_-._J_5-_2 .l:i ,: _J..._ _S

t

_i_.i i i iii _.

_

.

_,

, - _-. _-'a_mw

ii i i '.;: :_.' Fig. 10

.

Experimental frequency response measurements on

1OO __.

.

i i

'_ _

the 4.5-in (ll.4-cm) closed

-

box system of Fig. 9. The response

dB w_..-_

d

_ -' ..__ ___ was measured five different ways. a. In anechoic chamber in

___ _l,_ -i -._-._ farfield (4 _

r

sr). b. In anechoic chamber in driver's nearfield

C : _-_ - - --_ (4 _- st). c. On a 4- by 8-ft (1.2- by 2.4-m) baffle board, in

/

_

;t

_

_

_

_

_

0

__ chamber

,

in farfield (2 tr st). d. In lab on floor

,

m nearfield.

- NEAR ---_I_- FARFIELD : _11_11dl- .... _-

sc _'_'_'_-_-,--4-+_- _-_-"_4_ __]_- e. In box using the method of Small [11.

_l

d

*_

/

q-t-_ HALF-SPACE q_--[-- _r_l_ _--_

__1 _:2d--k-- __

,___t=]-_t--_--,_

,

7C -2 __ CONS .... e

' ;' I_ -

_(_

r

____,_ Frequency Response Measured by0g 200 500 tooo 2000 5000 10o00

2_.

,

1_300

D A B C Li_

f Hz

-

-

---

-

-

,.- Differ

ent M

ethods

Fig. 9. Experimental measurements performed to check Eq. The axial frequency response of the 4-in (11.4-Cb)

(7) and Fig. 4. The source is a 4.5-in (ll.4-cm) wide-range closed-box system, described in the previous section

,

was

driver, mounted in a 39

5

-ina (6473-cm a) closed box, flush measured using several different methods: 1) in the an-

mounted in the center of a 4- by 8-ft (1.2- by 2.4-m) sheet of echoic chamber in the driver's farfield (full space), 2) in

a

A

-in (1.9-Cb) plywood. Seven anechoic axial frequency re-

sponse measurements were made with the measurement micro- the anechoic chamber in the driver's nearfield (full space),

phone the indicated distance from the diaphragm. The dis- 3) in the anechoic chamber mounted on the 4- by 8-ft

tances chosen correspond to low-frequency axial attenuations (1.2- by 2.4-m) baffle board in the driver's farfield (half-

of 0, --5, --10

,

--15

,

--20

,

--25

,

and --30 dB relative to the

nearfield pressure at

r

= 0. space), 4) in the laboratory sitting on the test bench in the

driver's nearfield, and

5

) inside the test box enclosure

Several axial constant-voltage frequency responses were using Small's box-pressure measurement method [1].

taken at different distances from the driver, extending These test results are displayed in Fig. 10.

from the nearfield (

r

< 0.1l

a

) into the farfield (

r

> 5

a

Note the differences between the farfield responses of

for Iow frequencies). Distances corresponding to low- Fig. 10a and c that were measured in the 4 _r and 2 ,r eh-

frequency axial attenuations of 0, --5

,

-- 10

,

-- 15, --20

,

vironments. Diffraction effects and increasing cabinet

A

P

RIL 1

97

4, VOLUME 22, NUMBER

3

15

9


7/9

D

.

B

.

K

EE

L

E,

JR

.

directivity with frequency causes a rising characteristic in The nearfield measurement of the tweeter (Fig. 1 lc)

the response from about 100 to 800 Hz in the 4 _r space shows that its nearfield SPL is roughly 10 dB higher than

[9], [10]. that of the woofer. This level difference is expected be-

Keeping in mind the expected differences between Fig. cause the tweeter is roughly one third the diameter of the

10a and c, the frequency responses measured by the five woofer (assuming equal farfield SPL for each driver oper-

methods show good agreement below 500 Hz. A compar- sting in the piston range). The measured voice-coil re-

ison between the two indirect methods (Fig. 10d, e) resistance RB of the woofer is 4.8 ohms, and the calculated

veals that the nearfield technique yields accurate response efficiency for the level portion of the system low-fre-

data about 1 octaves higher than the box-pressure quency piston range (200-500 Hz)is 0.35%

technique.

._- _Vrms_=__'_I: --5= =- -I:---Z- _ _-- _

System Measurements ,lo --_$[= :5__-_i :__

To illustrate system measurements with the nearfield rtl _II-f}1_2= vt _

technique, two loudspeaker systems were measured, an 1OO_'_-_*_/-t Fr'' :----_[---_lI_;/RAGM OUT'

8-in (20.3-cm) two-wayclosed-boxacoustic suspension ...........

system and a 15-in (38.1-cm) three-way vented-box 9o_ .........____,__:________:_:: ___

system. SPI_ _ ____- -=/_4.__ _

Closed-Box

dB _

-

:_[

t

,

m

_s-'

_

'.::

-:

_

- _ .

The closed-box direct-radiator system consisted of an

8-in (20.3-cm) diameter (6.2-in (15.7-cm) effective piston _ 7=_:__ --_x_:i

diameter) high-compliance woofer, and a 21.._-in (6.4-cm) ,oo_ _,_-[:_-1_=_ _$____r__}:=__}___pu,_=_ _] .:__

diameter (2-in (5-em) effective diameter) closed-back go _+____,_j.+_.......

tweeter. : _+?--co_[A_-/i;__,. =---:

. __ , _t r.... ___[+_-___. --_-+_.::_.-

a Ft on axis :-t_ : __[.[=_'[_:{_-E_-::_ _::- f Hz_

;.

_=_'_:l_=_,_= =,_:

,

=_

_

=_5_=

-

:x

-

.;,7i Fig

.

12

.

Display of experi

m

en

t

al

m

easurements

t

aken

o

n

___:-. -/:--:...:::_ FARFIELD


8/9

L

OW-FR

E

QU

E

NCY LOUDSPEAK

E

R ASSESSM

E

NT BY NEARFIELD SO

U

ND-

P

R

E

S

SU

R

E

M

E

ASUREMENT

Fig. 8. The vent output (Fig. 12b) shows the effects of az> _ S/___.. = ./133

diaphragm crosstalk above 80 Hz when compared to Fig. 8. aV , , _/75- = 1.33.

[] Thisvaluecorrespondsto a farfieldpressurelevelshiftof

about +2.5 dB in favor of the diaphragm (for equal near-

field SPL, the diaphragm would contribute 2.5 dB more

level to the farfield pressure because of its larger size).

Examination of the nearfield responses for vent and

cone (Fig. 12a and b) reveals that the vent output at box

resonance (about 38 Hz) is down approximately 2 dB

from the diaphragm's output in the level response region

extending from 100 to 500 Hz. The total system output

is therefore down about 4.5 dB at 38 Hz. This single-point

output computation at /B, coupled with the knowledge

that the vented-box system rolls off at 24 dB per octave

below lB, was used with the measured cone output re-

sponse (Fig. 12a) to derive the approximate low-frequency

response in Fig. 14 (fa _- 41 Hz). The efficiency in level

portion of the piston-range response, from Fig. 7, is 3.1%

a

LEVEL

I

dB

2O m 50 l oo 5

00

1000 _

00

0

m

OO

W

000

f

Hz

Fig. 14. Approximate overall low-frequency response of

15-in (38.1-cm) vented-box system derived from measure-

m ents m ade using nearfield pressure sam pling technique (Fig.

12). The response indicates that system is slightly mistuned

from a 4th-order Butterw orth alignm ent at 40 Hz because the

box resonance frequency f_ is somewhat iow.

CONCL

U

SION

The theory presented, along with supporting experi-

,,, mental measurements,shows that loudspeakersystem

piston-range characteristics can easily be measured by

sampling the nearfield pressure with a test microphone

held close to the acoustic radiator. Valid nearfield mea-

surements may be taken in any reasonable environment.

without the use of an anechoic chamber or large outdoor

test site. Experimental measurements using the nearfield

technique show excellent agreement with more traditional

t es t me th od s.

APPENDIX

Expe r ime nta l Me a s u r ing Equ ipme nt

The following equipment was used in making the mea-

surements presented in this paper.

1) Beat frequency audio oscillator, Bruel and Kjaer

c (B K)ype1014.

Fig. 13.Nearfield measurements on assorted direct radiators 2) Power amplifier, 200 watt, Mclntosh, model MI-

in nonanechoic environment, a. Tweeter in 8-in (20.3-cm) two- 200AB.

way closed-box system (1/4-in (0.6-em) microphone), b. Woofer 3) Capacitor microphone, in, B&K type 4135 with

in 1 5-in (38.1 -cm ) ven ted -b ox sy stem , c. V ent in 1 5-in (38.1 -cm )

vented-boxystem, follower.

4) Capacitor microphone, in, B&K type 4133 with

An approximate overall low-frequency response was follower.

derived from these data by first computing the relative 5) Precision measurement amplifier, B&K type 2606.

size ratio between vent and driver diaphragm: 6) Graphic level recorder, B&K type 2305.

APRIL 1974, VOLUME 22, NUMBER 3 161


9/9

D. B. KEELE,JR.

Implementa

t

ion of Box

-

Pressur

e

Measur

e

m

e

n

t

s ments at Low Frequencies,"

7

.

Audio Eng

.

Soc

.

,

vol. 20,

pP. 28-33 (Jan.

/

Feb. 1972).

The frequency equalization network used to implement [2] L. E. Kinsler and A. R. Frey, Fundamentals o

Small's box-pressure measurement method [1] was cor-

Acoustics

(Wiley, New York

,

1962).

[3] J. Zemanek, Beam Behavior W ithin the Nearfield

rected only for the 1

/(o2

behavior [1, p. 29, eq. (2) and of a Vibrating Piston,"

J

. A

coust

.

Soc

.

A

m., vol. 49, pp.

(3)] of the box pressure. Box compliance shift and en- 181-191 (1971).

closure loss effects were not compensated for. A second- [4] N. W. McLachlan

, Loudspeaker Theory, Per/or

-

order high-pass RC filter, with corner frequency of 1 kHz

m

a

nce, Testing and Design

(Publications

,

New York

,

(

--

3 dB), was used to provide an approximate {

o

response 1960).

[5] R . H. Small, D irect-R adiator Loudspeaker System

up to about 1 kHz for these measurements. Analysis,"

J

.

Audio Eng

.

Soc

.

,

vol. 20, pp. 383-3

9

5 (Jun

e

1972).

ACKN

OW

LE

DG

MENT [6] J. E. Benson, "Theory and Design of Loudspeaker

Enclosures Part I: Electro-Acoustical Relations and Gen-

1 '

The author is indebted to Raymond J. Newman, Senior eralized Ana ysls, Amalgama ed Wireless Australasia)

Engineer, Loudspeaker Systems, at Electro-Voice, for Ltd. Tech. Rev., vol. 14, Pp. 1-57 (Aug. 1968).

[7] A . N. Thiele, Loudspeakers in Vented Boxes,

first making the observation that nearfield measurements

J

.

Audio Eng

.

Soc

., vol. 19, pp. 382-392 (May 1971); pp.

correlated well with anechoic measurements. (When the 471-483 (June 1

9

71).

author first joined Electro-Voice in June 1972, Ray had [8] J. E. Benson, Theory and Design of Loudspeaker

been making frequency response measurements using this Enclosures Part III: Introduction to Synthesis of Vented

method for about a year.) Systems," A.

W

.A.

Tech

.

Rev

.

,

vol. 14, pp. 369-484 (Nov.

The criticism and review of this manuscript by John 1972).

[9] II. F. Olson, "Direct Radiator Loudspeaker En-

Gilliom, Chief Product Engineer, Loudspeakers, at EV, closures,"

J

.

Audio Eng

.

Soc

.

,

vol. 17, pp. 22-2

9

(Jan.

and Ray Newman is gratefully acknowledged. The author 1969).

is further indebted to Dr. Richard H. Small of the Univer- [10] R. F. Allison and R. Berkovitz, "The Sound Field

sity of Sydney, Australia, for comments, suggested revi- in Home Listening Rooms,"

J

.

Audio Eng

.

Soc

.

,

vol. 20,

pp. 4

59

-469 (July

/

Aug. 1972).

sio ns, an d co nstructive criticism s o f th is p aper.

REFERENCES

No

t

e: Mr. Keele's biography appears in the lannary

/

Feb-

[1] R. II. Small, "Simplified Loudspeaker Measure- ruary 1973 issue of the Journal.

162 JOURNAL OF THEAUDIO ENGINEERING SOCIETY

Documents

Keele (1974-04 AES PublishLow-Frequency Loudspeaker Assessment by Nearfield Sound-Pressure Measuremented) - Nearfield Paper